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Parikh vectors
6KMJ_1 9HBF_1 3NVE_1 Letter Amino acid
3 1 2 M Methionine
5 2 0 P Proline
7 7 0 S Serine
6 15 0 T Threonine
1 2 0 C Cysteine
3 11 1 G Glycine
2 1 1 H Histidine
2 7 0 W Tryptophan
6 4 0 I Isoleucine
5 4 0 Y Tyrosine
5 3 0 R Arginine
3 1 0 Q Glutamine
8 3 0 D Aspartic acid
15 3 0 E Glutamic acid
8 1 0 L Leucine
10 4 0 K Lycine
7 1 1 F Phenylalanine
7 7 0 V Valine
4 8 0 A Alanine
5 6 1 N Asparagine 

6KMJ_1|Chain A|Nuclear protein STH1/NPS1|Saccharomyces cerevisiae (strain ATCC 204508 / S288c) (559292)
>9HBF_1|Chain A|Fucose-binding lectin protein|Ralstonia solanacearum (305)
>3NVE_1|Chains A, B|Major prion protein|Mesocricetus auratus (10036)
Protein code \(c\) LZ-complexity \(\mathrm{LZ}(w)\) Length \(n=|w|\) \(\frac{\mathrm{LZ}(w)}{n /\log_{20} n}\) \(p_w(1)\) \(p_w(2)\) \(p_w(3)\) Sequence \(w=f(c)\)
6KMJ , Knot 61 112 0.85 40 95 109 
SLGIFPTVEKLVEEMREQLDEVDSHPRTSIFEKLPSKRDYPDYFKVIEKPMAIDIILKNCKNGTYKTLEEVRQALQTMFENARFYNEEGSWVYVDADKLNEFTDEWFKEHSS
9HBF , Knot 44 91 0.72 40 66 82 
MKSVQTAATSWGTVPSIRVYTANNGKITERCWDGKGWYTGAFNEPGDNVSVTSWLVGSAIHIRVYASTGTTTTEWCWDGNGWTKGAYTATN
3NVE , Knot 5 6 0.49 10 5 4 
MMHFGN

Let \(P_w(n)\) be the set of distinct subwords (intervals) in a word \(w\). Let \(p_w(n)\) be the cardinality of \(P_w(n)\). Let \(f(c)\) be the sequence in FASTA with 4-symbol Protein Data Bank code \(c\).

\(|P_{f(6KMJ_1)}(2) \setminus P_{f(9HBF_1)}(2)|=81\), \(|P_{f(9HBF_1)}(2) \setminus P_{f(6KMJ_1)}(2)|=52\). Let \( Z_k(x,y)=|P_x(k)\setminus P_y(k)|+|P_y(k)\setminus P_x(k)| \) be a LZ76 style (set of subwords) Jaccard distance numerator for \(P(k)\).Hydrophobic-polar version of Sequence 1:0111110100110010001001000100011001100000100101100111101110000010000100100110011001010000101101010010010001100000
Pair \(Z_2\) Length of longest common subsequence
6KMJ_1,9HBF_1 133 2
6KMJ_1,3NVE_1 100 1
9HBF_1,3NVE_1 69 2

Newick tree

 
[
	6KMJ_1:64.94,
	[
		3NVE_1:34.5,9HBF_1:34.5
	]:30.44
]

Let d be the Otu--Sayood distance d.
Let d1 be the Otu--Sayood distance d1. (This makes the 4TYN sequence AAAAAA a close match...)
A roughly speaking expected distance is \((0.85)(0.8)(\frac{203 }{\log_{20} 203}-\frac{91}{\log_{20}91})=36.7\)
Status Protein1 Protein2 d d1/2
Query variables 6KMJ_1 9HBF_1 50 43
Was not able to put for d
Was not able to put for d1

In notation analogous to [Theorem 16, Kjos-Hanssen, Niraula and Yoon (2022)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]